The Duke and Duchess of Cambridge are so competitive that they rarely finish a
game of Scrabble because one of them will upset the board in a huff, the
Duchess has disclosed.

The couple have shown in the past that when they are pitted against each other, such as during a dragon boat race in Canada, neither gives any quarter.

And the Duchess told the Olympic boxer Anthony Ogogo that their intense rivalry even extends to board games.

In the ITV documentary Our Queen, which will be broadcast on Sunday, the bronze medallist recounted a conversation moments after to speaking to the Duchess at a Buckingham Palace reception for Team GB athletes.

He said: “She told me that when William and her play Scrabble they don’t usually finish it because one of them slams it shut.”

The Duke and Duchess had fresh chances to best each other today when they arrived at Cheltenham Festival for a day’s racing, where they are likely to keep tally of who wins the most money.

The Duchess, who is around five months pregnant, wore a light brown double-breasted coat with chocolate coloured trousers, hat, gloves and clutch bag, together with dark calf-length boots.

They were joined at the meeting by the Princess Royal, with Zara Phillips and her husband Mike Tindall, who has an interest in one of the runners, expected to arrive later.

The ITV documentary, filmed during the Queen’s Diamond Jubilee year, provides a series of fascinating glimpses into Royal life, including one of the monarch’s favourite tricks to surprise visiting heads of state.

The Queen likes to hide a microphone in floral arrangements so it will not spoil the splendour of the table at a State banquet when it is required for the official speeches.

As she inspects the table settings in the ballroom at Buckingham Palace before one such visit, she asks one of her staff: “Where have you hidden it this time? They’re always mystified when I say ‘It’s perfectly alright, just speak’.”

The Countess of Wessex, interviewed on camera for the first time since she married Prince Edward in 1999, reveals how difficult it can be even for members of the Royal family to get used to the logistics of state visits.

She said: “The moment you go into the ballroom at Buckingham Palace, actually it’s terrifying. On more than one occasion I have sat in the wrong seat.”

Up to 180 guests are typically seated around tables arranged in a horseshoe, and the Countess continued: “I’ll never forget the look I got [from the Queen] when I couldn’t find my chair and she was waiting to start her speech.”

Discussing the Queen’s memorable appearance with Daniel Craig’s James Bond during the opening ceremony of London 2012, during which the Queen appeared to parachute out of a helicopter, Lord Coe disclosed his fears that the stunt would appear undignified.

He said: “When Danny Boyle came to see us and said ‘I’ve got this great idea about the Queen jumping out of a helicopter, it’s a pretty bizarre departure point.

“Respect was our watchword. We had to be sure this didn’t descend into It’s a Royal Knockout.”

He added that as a stuntman dressed as the Queen jumped from a chopper, Princes William and Harry shouted “Go granny”.

Princess Eugenie said the Queen had not told her grandchildren about it before the public saw it, and when she asked her about later: “She just said ‘yeah, it was fun’, like water off a duck’s back.”

But while the Queen knows who James Bond is, she is less familiar with pop stars. After meeting the Queen backstage after a Royal Variety Performance, Robbie Williams said: “She asked me: ‘Were you the gentleman on the wires?’ She thought I was someone else.”

The film also features an interview with David Cameron, who says of his visits to Balmoral: “There’s not much chillaxing at Balmoral. They’re fairly active even though they’re on holiday.”